Building materials and products - Hygrothermal properties -Tabulated design values and procedures for determining declared and design thermal values (ISO 10456:2007)

ISO 10456:2007 specifies methods for the determination of declared and design thermal values for thermally homogeneous building materials and products, together with procedures to convert values obtained under one set of conditions to those valid for another set of conditions. These procedures are valid for design ambient temperatures between -30 °C and +60 °C.
ISO 10456:2007 provides conversion coefficients for temperature and for moisture. These coefficients are valid for mean temperatures between 0 °C and 30 °C.
ISO 10456:2007 also provides design data in tabular form for use in heat and moisture transfer calculations, for thermally homogeneous materials and products commonly used in building construction.

Baustoffe und Bauprodukte - Wärme- und feuchtetechnische Eigenschaften - Tabellierte Bemessungswerte und Verfahren zur Bestimmung der wärmeschutztechnischen Nenn- und Bemessungswerte (ISO 10456:2007)

Diese Internationale Norm legt Verfahren zur Bestimmung der wärmeschutztechnischen Nenn  und Bemes¬sungswerte von wärmetechnisch homogenen Baustoffen und -produkten fest und enthält Verfahren zur Umrechnung von Werten, die unter einem Satz von Bedingungen erhalten wurden, in solche Werte, die für einen anderen Satz von Bedingungen gelten. Diese Verfahren sind auf Bemessungsumgebungs¬temperaturen zwischen -30 °C und +60 °C anwendbar.
Die Internationale Norm liefert Umrechnungskoeffizienten für die Temperatur und die Feuchte. Diese Koeffizienten gelten für Mitteltemperaturen zwischen 0 °C und 30 °C.
Darüber hinaus enthält die Norm in Tabellenform Bemessungsdaten für die Anwendung in Berechnungen der Wärme  und Feuchteübertragung für wärmetechnisch homogene Baustoffe und -produkte, die üblicherweise im Hochbau eingesetzt werden.

Matériaux et produits pour le bâtiment - Propriétés hygrothermiques - Valeurs utiles tabulées et procédures pour la détermination des valeurs thermiques déclarées et utiles (ISO 10456:2007)

L'ISO 10456:2007 spécifie des méthodes pour la détermination des valeurs thermiques déclarées et utiles des matériaux et produits du bâtiment thermiquement homogènes, ainsi que des procédures pour convertir les valeurs obtenues pour un ensemble de conditions en valeurs valides pour un autre ensemble de conditions. Ces procédures sont valables pour des températures ambiantes utiles comprises entre -30 °C et +60 °C.
L'ISO 10456:2007 fournit les coefficients de conversion liés à la température et à l'humidité. Ces coefficients sont valables pour des températures moyennes comprises entre 0 °C et 30 °C.
L'ISO 10456:2007 fournit également les valeurs utiles tabulées nécessaires aux calculs des transferts de chaleur et d'humidité des matériaux et produits thermiquement homogènes couramment utilisés dans la construction.

Gradbeni materiali in proizvodi - Higrotermalne lastnosti - Tabelirane računske vrednosti in postopki za določevanje nazivnih in računskih vrednosti toplotnih vrednosti (ISO 10456:2007)

Ta mednarodni standard določa metode za ugotavljanje nazivnih in računskih vrednosti toplotnih vrednosti za toplotno homogene gradbene materiale in proizvode, in postopke za pretvarjanje vrednosti, pridobljenih pod enim naborom pogojem, v vrednosti, ki veljajo pod drugim naborom pogojev. Ti postopki veljajo za računske temperature okolja med 30°C in 60°C. Ta mednarodni standard določa pretvorbene koeficiente za temperaturo in vlago. Ti koeficienti veljajo za povprečne temperature med 0°C in 30°C. Ta mednarodni standard zagotavlja tudi računske podatke v tabelarični obliki, namenjene izračunom prenosa vročine in vlage za toplotno homogene materiale in proizvode, ki se pogosto uporabljajo v gradbeništvu.

General Information

Status
Published
Publication Date
14-Dec-2007
Current Stage
6060 - Definitive text made available (DAV) - Publishing
Due Date
15-Dec-2007
Completion Date
15-Dec-2007

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SLOVENSKI STANDARD
SIST EN ISO 10456:2008
01-maj-2008
1DGRPHãþD
SIST EN 12524:2001
SIST EN ISO 10456:2001
*UDGEHQLPDWHULDOLLQSURL]YRGL+LJURWHUPDOQHODVWQRVWL7DEHOLUDQHUDþXQVNH
YUHGQRVWLLQSRVWRSNL]DGRORþHYDQMHQD]LYQLKLQUDþXQVNLKYUHGQRVWLWRSORWQLK
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Building materials and products - Hygrothermal properties -Tabulated design values and

procedures for determining declared and design thermal values (ISO 10456:2007)

Baustoffe und ­produkte - Wärme­ und feuchtetechnische Eigenschaften - Tabellierte

Bemessungswerte und Verfahren zur Bestimmung der wärmeschutztechnischen Nenn­
und Bemessungswerte (ISO 10456:2007)

Matériaux et produits du bâtiment - Propriétés hygrothermiques - Tableaux des valeurs

de conception et procédures pour la détermination des valeurs thermiques déclarées et

de conception (ISO 10456:2007)
Ta slovenski standard je istoveten z: EN ISO 10456:2007
ICS:
91.100.01 Gradbeni materiali na Construction materials in
splošno general
91.120.10 Toplotna izolacija stavb Thermal insulation
SIST EN ISO 10456:2008 en

2003-01.Slovenski inštitut za standardizacijo. Razmnoževanje celote ali delov tega standarda ni dovoljeno.

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SIST EN ISO 10456:2008
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SIST EN ISO 10456:2008
EUROPEAN STANDARD
EN ISO 10456
NORME EUROPÉENNE
EUROPÄISCHE NORM
December 2007
ICS 91.120.10 Supersedes EN ISO 10456:1999
English Version
Building materials and products - Hygrothermal properties -
Tabulated design values and procedures for determining
declared and design thermal values (ISO 10456:2007)

Matériaux et produits pour le bâtiment - Propriétés Baustoffe und Bauprodukte - Wärme- und

hygrothermiques - Valeurs utiles tabulées et procédures feuchtetechnische Eigenschaften - Tabellierte

pour la détermination des valeurs thermiques déclarées et Bemessungswerte und Verfahren zur Bestimmung der

utiles (ISO 10456:2007) wärmeschutztechnischen Nenn- und Bemessungswerte
(ISO 10456:2007)
This European Standard was approved by CEN on 7 December 2007.

CEN members are bound to comply with the CEN/CENELEC Internal Regulations which stipulate the conditions for giving this European

Standard the status of a national standard without any alteration. Up-to-date lists and bibliographical references concerning such national

standards may be obtained on application to the CEN Management Centre or to any CEN member.

This European Standard exists in three official versions (English, French, German). A version in any other language made by translation

under the responsibility of a CEN member into its own language and notified to the CEN Management Centre has the same status as the

official versions.

CEN members are the national standards bodies of Austria, Belgium, Bulgaria, Cyprus, Czech Republic, Denmark, Estonia, Finland,

France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia, Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal,

Romania, Slovakia, Slovenia, Spain, Sweden, Switzerland and United Kingdom.
EUROPEAN COMMITTEE FOR STANDARDIZATION
COMITÉ EUROPÉEN DE NORMALISATION
EUROPÄISCHES KOMITEE FÜR NORMUNG
Management Centre: rue de Stassart, 36 B-1050 Brussels

© 2007 CEN All rights of exploitation in any form and by any means reserved Ref. No. EN ISO 10456:2007: E

worldwide for CEN national Members.
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SIST EN ISO 10456:2008
EN ISO 10456:2007 (E)
Contents Page

Foreword..............................................................................................................................................................3

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SIST EN ISO 10456:2008
EN ISO 10456:2007 (E)
Foreword

This document (EN ISO 10456:2007) has been prepared by Technical Committee ISO/TC 163 "Thermal

performance and energy use in the built environment" in collaboration with Technical Committee CEN/TC 89

"Thermal performance of buildings and building components", the secretariat of which is held by SIS.

This European Standard shall be given the status of a national standard, either by publication of an identical

text or by endorsement, at the latest by June 2008, and conflicting national standards shall be withdrawn at

the latest by June 2008.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

rights. CEN [and/or CENELEC] shall not be held responsible for identifying any or all such patent rights.

This document supersedes EN ISO 10456:1999.

According to the CEN/CENELEC Internal Regulations, the national standards organizations of the following

countries are bound to implement this European Standard: Austria, Belgium, Bulgaria, Cyprus, Czech

Republic, Denmark, Estonia, Finland, France, Germany, Greece, Hungary, Iceland, Ireland, Italy, Latvia,

Lithuania, Luxembourg, Malta, Netherlands, Norway, Poland, Portugal, Romania, Slovakia, Slovenia, Spain,

Sweden, Switzerland and the United Kingdom.
Endorsement notice

The text of ISO 10456:2007 has been approved by CEN as a EN ISO 10456:2007 without any modification.

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SIST EN ISO 10456:2008
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SIST EN ISO 10456:2008
INTERNATIONAL ISO
STANDARD 10456
Third edition
2007-12-15
Building materials and products —
Hygrothermal properties — Tabulated
design values and procedures for
determining declared and design thermal
values
Matériaux et produits pour le bâtiment — Propriétés hygrothermiques —
Valeurs utiles tabulées et procédures pour la détermination des valeurs
thermiques déclarées et utiles
Reference number
ISO 10456:2007(E)
ISO 2007
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
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COPYRIGHT PROTECTED DOCUMENT
© ISO 2007

All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means,

electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or

ISO's member body in the country of the requester.
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Published in Switzerland
ii © ISO 2007 – All rights reserved
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
Contents Page

Foreword............................................................................................................................................................ iv

Introduction ........................................................................................................................................................ v

1 Scope ..................................................................................................................................................... 1

2 Normative references ........................................................................................................................... 1

3 Terms, definitions, symbols and units ............................................................................................... 1

3.1 Terms and definitions........................................................................................................................... 1

3.2 Symbols and units................................................................................................................................ 2

4 Test methods and test conditions ...................................................................................................... 3

4.1 Tests for thermal properties ................................................................................................................ 3

4.2 Tests for moisture properties.............................................................................................................. 3

5 Determination of declared thermal values ......................................................................................... 3

6 Determination of design thermal values ............................................................................................ 4

6.1 General................................................................................................................................................... 4

6.2 Rounding of design values.................................................................................................................. 4

6.3 Design values derived from declared values..................................................................................... 5

6.4 Design values derived from measured values .................................................................................. 5

7 Conversion of thermal values ............................................................................................................. 5

7.1 General................................................................................................................................................... 5

7.2 Conversion for temperature ................................................................................................................ 5

7.3 Conversion for moisture ...................................................................................................................... 6

7.4 Age conversion ..................................................................................................................................... 6

7.5 Natural convection................................................................................................................................ 6

8 Tabulated design hygrothermal values.............................................................................................. 8

8.1 General................................................................................................................................................... 8

8.2 Design thermal values.......................................................................................................................... 8

8.3 Design moisture values ....................................................................................................................... 8

Annex A (normative) Conversion coefficients for temperature .................................................................. 15

Annex B (informative) Examples of calculations .......................................................................................... 19

Annex C (informative) Statistical calculations .............................................................................................. 22

Bibliography ..................................................................................................................................................... 24

© ISO 2007 – All rights reserved iii
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
Foreword

ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies

(ISO member bodies). The work of preparing International Standards is normally carried out through ISO

technical committees. Each member body interested in a subject for which a technical committee has been

established has the right to be represented on that committee. International organizations, governmental and

non-governmental, in liaison with ISO, also take part in the work. ISO collaborates closely with the

International Electrotechnical Commission (IEC) on all matters of electrotechnical standardization.

International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 2.

The main task of technical committees is to prepare International Standards. Draft International Standards

adopted by the technical committees are circulated to the member bodies for voting. Publication as an

International Standard requires approval by at least 75 % of the member bodies casting a vote.

Attention is drawn to the possibility that some of the elements of this document may be the subject of patent

rights. ISO shall not be held responsible for identifying any or all such patent rights.

ISO 10456 was prepared by Technical Committee ISO/TC 163, Thermal performance and energy use in the

built environment, Subcommittee SC 2, Calculation methods.

This third edition cancels and replaces the second edition (ISO 10456:1999), which has been technically

revised.
The following changes have been made to the second edition:

⎯ the Scope has been extended to include tabulated design values of thermal and moisture properties of

materials, and the title has been modified accordingly;
⎯ an Introduction has been added;

⎯ the Scope specifies that moisture coefficients are valid only between 0 °C and 30 °C;

⎯ 4.2 has been added as a new subclause on tests for moisture properties;
⎯ 7.2 has been extended to contain general information about climates;

⎯ 7.4 contains clarification that ageing factors are not applied if taken into account in declared values;

⎯ 7.5 has been added as a new subclause dealing with convection in insulating materials;

⎯ Clause 8 has been added, giving tabulated design values (in Tables 3, 4 and 5); the data, taken from

EN 12524, have been reviewed and updated.

⎯ Annex A contains data reviewed for extruded polystyrene (XPS) and polyurethane (PU).

iv © ISO 2007 – All rights reserved
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
Introduction

This International Standard provides the means (in part) to assess the contribution that building products and

services make to energy conservation and to the overall energy performance of buildings.

Heat and moisture transfer calculations require design values of thermal and moisture properties for materials

used in building applications.

Design values can be derived from declared values that are based on measured data on the product

concerned, which is usually the case for thermal insulation materials. Where the design conditions differ from

those of the declared value, the data needs to be converted to the applicable conditions. This International

Standard provides the methods and data for making this conversion.

For materials for which measured values are not available, design values can be obtained from tables. This

International Standard provides such tabulated information based on the compilation of existing data (see

reference documents listed in the Bibliography).
© ISO 2007 – All rights reserved v
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SIST EN ISO 10456:2008
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SIST EN ISO 10456:2008
INTERNATIONAL STANDARD ISO 10456:2007(E)
Building materials and products — Hygrothermal properties —
Tabulated design values and procedures for determining
declared and design thermal values
1 Scope

This International Standard specifies methods for the determination of declared and design thermal values for

thermally homogeneous building materials and products, together with procedures to convert values obtained

under one set of conditions to those valid for another set of conditions. These procedures are valid for design

ambient temperatures between −30 °C and +60 °C.

This International Standard provides conversion coefficients for temperature and for moisture. These

coefficients are valid for mean temperatures between 0 °C and 30 °C.

This International Standard also provides design data in tabular form for use in heat and moisture transfer

calculations, for thermally homogeneous materials and products commonly used in building construction.

2 Normative references

The following referenced documents are indispensable for the application of this document. For dated

references, only the edition cited applies. For undated references, the latest edition of the referenced

document (including any amendments) applies.
ISO 7345, Thermal insulation — Physical quantities and definitions

ISO 8990, Thermal insulation — Determination of steady-state thermal transmission properties — Calibrated

and guarded hot box

ISO 12572, Hygrothermal performance of building materials and products — Determination of water vapour

transmission properties
3 Terms, definitions, symbols and units
3.1 Terms and definitions

For the purposes of this document, the terms and definitions given in ISO 7345 and the following apply.

3.1.1
declared thermal value

expected value of a thermal property of a building material or product assessed from measured data at

reference conditions of temperature and humidity, given for a stated fraction and confidence level, and

corresponding to a reasonable expected service lifetime under normal conditions
3.1.2
design thermal value
design thermal conductivity or design thermal resistance

NOTE A given product can have more than one design value, for different applications or environmental conditions.

© ISO 2007 – All rights reserved 1
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
3.1.3
design thermal conductivity

value of thermal conductivity of a building material or product under specific external and internal conditions,

which can be considered as typical of the performance of that material or product when incorporated in a

building component
3.1.4
design thermal resistance

value of thermal resistance of a building product under specific external and internal conditions, which can be

considered as typical of the performance of that product when incorporated in a building component

3.1.5
material

piece of a product irrespective of its delivery form, shape and dimensions, without any facing or coating

3.1.6
product

final form of a material ready for use, of given shape and dimensions and including any facings or coatings

3.2 Symbols and units
Symbol Quantity Unit
c specific heat capacity at constant pressure J/(kg⋅K)
F ageing conversion factor —
F moisture conversion factor —
F temperature conversion factor —
f temperature conversion coefficient K
f moisture conversion coefficient mass by mass kg/kg
a 3 3
f moisture conversion coefficient volume by volume m /m
R thermal resistance m ⋅K/W
s water vapour diffusion-equivalent air layer thickness m
T thermodynamic temperature K
u moisture content mass by mass kg/kg
λ thermal conductivity W/(m⋅K)
µ water vapour resistance factor —
ρ density kg/m
3 3
ψ moisture content volume by volume m /m
For conversion of thermal properties.
2 © ISO 2007 – All rights reserved
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
4 Test methods and test conditions
4.1 Tests for thermal properties
4.1.1 Test methods

Measured values of thermal conductivity or thermal resistance shall be obtained using the following methods:

⎯ guarded hot plate, in accordance with ISO 8302 or equivalent national method;
⎯ heat flow meter, in accordance with ISO 8301 or equivalent national method;
⎯ calibrated and guarded hot box, in accordance with ISO 8990.
4.1.2 Test conditions

To avoid conversions, it is recommended that measurements be conducted under conditions corresponding to

the selected set of conditions given in Table 1.

The mean test temperature should be chosen so that the application of the temperature coefficients does not

introduce a change of more than 2 % from the measured value.
The following testing conditions are required:
⎯ measured thickness and density for identification;
⎯ mean test temperature;
⎯ moisture content of the specimen during test;

⎯ (for aged materials) age of the specimen and conditioning procedures before testing.

4.2 Tests for moisture properties

Measured values of water vapour resistance factor or water vapour diffusion-equivalent air layer thickness

shall be obtained using ISO 12572.
5 Determination of declared thermal values

A declared thermal value shall be given under one of the sets of conditions a) or b) in Table 1, with reference

temperature I (10 °C) or II (23 °C).
Table 1 — Declared value conditions
Sets of conditions
Property
I (10 °C) II (23 °C)
a) b) a) b)
Reference temperature 10 °C 10 °C 23 °C 23 °C
a b a b
Moisture u u u u
dry 23,50 dry 23,50
Ageing aged aged aged aged

u is a low moisture content reached by drying according to specifications or standards for the material concerned.

dry

u is the moisture content when in equilibrium with air at 23 °C and relative humidity of 50 %.

23,50
© ISO 2007 – All rights reserved 3
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SIST EN ISO 10456:2008
ISO 10456:2007(E)

Either the declared value shall be determined at a thickness large enough to neglect the thickness effect, or

the declared values for smaller thicknesses shall be based on measurements at those thicknesses.

The data used shall be either
⎯ directly measured values according to the test methods given in Clause 4, or

⎯ obtained indirectly by making use of an established correlation with a related property such as density.

When all data have not been measured under the same set of conditions, they shall first be brought to one set

of conditions (see Clause 7). A statistical single value estimate shall then be calculated. Annex C refers to

International Standards on statistics that may be used.

During calculations, no value shall be rounded to less than three significant figures.

The declared value is the estimated value of the statistical single value, rounded according to either or both of

the following rules:
a) for thermal conductivity, λ, expressed in W/(m⋅K):
⎯ if λu 0,08: rounding to nearest higher 0,001 W/(m⋅K);
⎯ if 0,08 < λu0,20: rounding to nearest higher 0,005 W/(m⋅K);
⎯ if 0,20 < λu2,00: rounding to nearest higher 0,01 W/(m⋅K);
⎯ if 2,00 < λ : rounding to nearest higher 0,1 W/(m⋅K);

b) for thermal resistance, R, expressed in m ⋅K/W, as the nearest lower value rounded to not more than two

decimals or three significant figures.

Rules for determining declared values for specific products may be specified in applicable product standards.

6 Determination of design thermal values
6.1 General

Design values can be obtained from declared values, measured values or tabulated values (see Clause 8).

Measured data shall be either

⎯ directly measured values in accordance with the test methods given in Clause 4, or

⎯ obtained indirectly by making use of an established correlation with a related property, such as density.

If the set of conditions for declared, measured or tabulated values can be considered relevant for the actual

application, those values can be used directly as design values. Otherwise, conversion of data shall be

undertaken according to the procedure given in Clause 7.
6.2 Rounding of design values

The design value shall be rounded in accordance with the rules given in Clause 5:

⎯ for thermal conductivity, as the nearest higher value, in W/(m⋅K);
⎯ for thermal resistance, as the nearest lower value, in m ⋅K/W.
4 © ISO 2007 – All rights reserved
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
6.3 Design values derived from declared values

When the design value is calculated from the declared value and is based on the same statistical evaluation,

the declared value shall be converted to the design conditions.

Information is given in Annex C on how to derive design values based on another statistical evaluation

different from the one applicable to the declared value.
6.4 Design values derived from measured values

When necessary, all data shall first be converted to the design conditions. A statistical single value estimate

shall then be calculated. Annex C refers to International Standards on statistics that can be used.

7 Conversion of thermal values
7.1 General

Conversions of thermal values from one set of conditions (λ , R ) to another set of conditions (λ , R ) are

1 1 2 2
carried out according to the following equations:
λλ= F FF (1)
21mT a
R = (2)
F FF
T ma

Conversion coefficients may be taken from the applicable tables in this International Standard. Alternatively,

they may be derived from measured data obtained in accordance with the test methods referred to in 4.1,

provided that the procedure for determining conversion coefficients other than those in Table 4 are validated

by independent test institutes.
7.2 Conversion for temperature
The factor F for temperature is determined by
fT()−T
T 21
F = e (3)
where
f is the temperature conversion coefficient;
T is the temperature of the first set of conditions;
T is the temperature of the second set of conditions.

Values of the temperature conversion coefficient for insulation materials and masonry materials are given in

Annex A.

NOTE The effect of temperature on the thermal properties of other materials is generally not significant for heat

transfer calculations, and can usually be neglected.

Design thermal values should be obtained for the expected mean temperature of the material as installed in

the component in the applicable climate.
© ISO 2007 – All rights reserved 5
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
7.3 Conversion for moisture
The factor F for moisture content is determined as follows:
a) conversion of moisture content given as mass by mass:
fu()−u
u 21
F = e (4)
where
f is the moisture conversion coefficient mass by mass;
u is the moisture content mass by mass of the first set of conditions;
u is the moisture content mass by mass of the second set of conditions;
b) conversion of moisture content given as volume by volume:
f()ψ −ψ
ψ 21
F = e (5)
where
f is the moisture conversion coefficient volume by volume;
ψ is the moisture content volume by volume of the first set of conditions;
ψ is the moisture content volume by volume of the second set of conditions.

Values of the moisture conversion coefficient for insulation and masonry materials are given in Table 4.

7.4 Age conversion

The ageing depends upon the material type, facings, structures, the blowing agent, the temperature and the

thickness of the material. For a given material, the ageing effect can be obtained from theoretical models

validated by experimental data. There are no simple rules to correlate ageing over time for a given material.

If the declared thermal value takes account of ageing, no further ageing conversions shall be applied for

design thermal values.

If a conversion factor F is used, it shall allow the calculation of the aged value of the thermal property

corresponding to a time not less than half the working lifetime of the product in the application concerned.

NOTE 1 The working lifetime is often taken as 50 years.

NOTE 2 No conversion coefficients are given in this International Standard to derive the ageing conversion factor F .

Procedures for establishing aged values or ageing factors are given in some product standards.

7.5 Natural convection

The onset of natural convection in an insulating material with an open structure depends on permeability,

thickness and temperature difference. The driving force for natural convection is described by the modified

Rayleigh number, Ra , which is a dimensionless number defined for the purposes of this International

Standard by
dk∆T
Ra =×310 (6)
6 © ISO 2007 – All rights reserved
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SIST EN ISO 10456:2008
ISO 10456:2007(E)
where
∆T is the temperature difference across the insulation, in K;
d is the thickness of the insulation, in m;
k is the permeability of the insulation, in m ;
λ is the thermal conductivity of the insulation without convection, in W/(m⋅K).

If Ra does not exceed the critical value in Table 2, no correction for natural convection shall be made.

NOTE 1 The formal definition of Ra is
gcβρ
dk∆T
Ra=× (7)
ν λ
where
g is the acceleration due to gravity (9,81 m/s );
β is the thermal expansion coefficient for air;
ρ is the density for air;
c is the specific heat capacity for air at constant pressure;

ν is the kinematic viscosity for air (equal to dynamic viscosity divided by density).

Equation (6) is obtained by substituting the properties for air at 10 °C given in ISO 10292.

NOTE 2 Permeability is defined for one-dimensional steady-state conditions by the equation:

∆P η V
=× (8)
dk A
where
∆P is the pressure difference;
η is the dynamic viscosity of air;
...

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